2 Answers
2

I'll try to explain がる and がっている more generally, and then conclude with a direct answer about たがる and たがっている.

As stated in When to use 欲しがる instead of 欲しい, it is strange to talk directly about the mental state of someone else. がる provides one medium for discussing your conjecture about another persons mental state, and roughly means "shows signs of X". It is used specifically with ～ほしい, ～たい, and adjectives relating to emotion (often called personal predicates).

たけしさんは食べたがっている。Takeshi is showing signs of wanting to eat.
兄は車をほしがっている。My older brother is showing signs of wanting a car.
彼はうれしがっている。He is showing signs of being happy.

Generally, the difference between がる and がっている resembles the difference between the non-past and ている forms in other verbs.

It seems that especially with たい and ほしい, がる and がっている can introduce some new subtlety. Consider the following:

車をほしがる。He wants a car.
車をほしがっている。He wants a car.

On the surface, both seem to simply mean that he wants a car. However, there is a little more to it, ほしがる conveys a sense that he wants a car in general, but right now, it may not be his top priority. At the present moment, he's probably showing signs of something else (maybe he looks sad because his test grade was low!). On the other hand, ほしがっている conveys a sense of immediacy and importance. If he ほしがっている's, he is probably either showing signs of it right now or he wants it enough in general that he would ほしがる it pretty often. Regardless of which you choose, at the present point in time, he wants the car.

Here's how you can keep it all straight. Remember the literal translation of がる? "To show signs of wanting"

車をほしがる。He shows signs of wanting a car.
車をほしがっている。He is showing signs of wanting a car.

Disclaimer: My experience with this form is not extensive, and I'm drawing pretty heavily on intuition (from a very modest amount of experience). I hope someone else can make sure I haven't misrepresented anything or left anything out.

がった: Was showing signs of ~. Whether or not the person is currently showing signs of ~ has yet to be verified.

がっていた: Was showing signs of ~ for an indeterminate period(Unless a time range is specified). Person is currently not showing signs of ~.

~たがる:

~たがる: [is showing]/[will show] signs of wanting to do ~

~たがっている: continued state of showing signs of wanting to do ~

~たがった: Was showing signs of wanting to do ~. Whether or not the person is currently showing signs of wanting to do ~ has yet to be verified.

~たがっていた: Was showing signs of wanting to do ~ for an indeterminate period(Unless a time range is specified). Person is currently not showing signs of wanting to do ~.

~ほしがる:

[Noun] を ほしがる: to appear to want [Noun]

[Noun] を ほしがっている: continued state of appearing to want [Noun]

[Noun] を ほしがった: appeared to want [Noun]

[Noun] を ほしがっていた: had appeared to want [Noun]

I would deduce that the choice between ~がる and ~がっている would be affected by the time when you as a first person observes when the other party starts to "show signs of ~"

For ~がる: The time when you as a first person observes the other party and makes the statement based on your deduction that he currently appears to show signs of ~

For ~がっている: You as a first person has observed at some indeterminate time in the past, that the other party had shown signs of ~ and further deduced that the other party's state continues up to the point of you making the statement.

Now to put it into examples:

Let's say I'm meeting up with a friend(Let's name him Jim) and both of us walk past a store, and I notice that Jim is looking earnestly at something in the store window. In this case I would use がる to describe Jim's behaviour.

Now suppose some time has elapsed, and I discuss 1. with another person. My previous memory tells me that Jim had shown that he wanted a particular thing from the store, and I surmise that his want carries on to the present moment. I would use がっている to describe Jim's behaviour.

Disclaimer: The above are extrapolations based on what I know about verb-plain/verb-ている and verb-plain/verb-past. Please do not hesitate to correct me.
– Flaw♦Oct 4 '11 at 5:10

Disagree with 1. Verbs ending in がる are non-stative, so the plain がる form expresses habituality or future tense. I don't think either fits the situation you describe. It should be がっている.
– dainichiAug 22 '12 at 0:08